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Experimental Mathematics Seminar

Games Played Randomly-Chomp and Nim

Pat Devlin and Paulina Trifonova, Swarthmore College

Location:  https://rutgers.zoom.us/j/91865817691 [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Date & time: Thursday, 21 November 2024 at 5:00PM - 6:00PM

Abstract: In this talk, we discuss combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random), and we will emphasize the "experimental math" approach that was the backbone of our results. We provide closed-form expressions for the expected number of turns in a game of Chomp with any starting condition. We also derive and prove formulas for the win probabilities for any game of Chomp with at most two rows. Additionally, we completely analyze the game of nim under random play by finding the expected number of turns and win probabilities from any starting position. No familiarity with probability is required, as the talk quickly reduces to studying certain recurrence relations that naturally arise from each game